Mathematics

Solve $$\displaystyle\int\dfrac {\sin x}{(1+\cos x)^{2}}dx$$


SOLUTION
$$\displaystyle\int\dfrac {\sin x}{(1+\cos x)^{2}}dx$$
Put, $$ 1 + \cos x  = t $$

$$\implies - \sin x dx = dt$$

Now, $$\displaystyle\int \dfrac{\sin x}{(1 + \cos x)^{2}} dx = \int \dfrac{-1}{t^2} dt$$

$$ = -\int t^{-2} dt = - (\dfrac{t^{-1}}{-2+1}) + c$$

$$= \dfrac{1}{t} + c$$

$$ = \dfrac{1}{1 + \cos x} + c$$
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Subjective Medium Published on 17th 09, 2020
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